If the trick from Majesty does not work for you or mayer's answer did not change anything but you found a lot of corrosion on your logic board, I'd go with that. Go ahead and clean with a high grade (preferably over 90%)isopropyl alcohol and a brush, just be careful not to knock off any components of the board. Also pay good attention to the connectors and ribbon cable. I have seen the ends of the cable literally green with oxidation. After that dry it well, yes you can use a hair dryer on the cold settings to expedite that process. Re-assemble and give it a try and see what you got. BTW if you already have it open do yourself a favor and replace the battery so you do not have to mess with it at a later time. Good Luck and let us know.

iPod Nano 5 gen has a DFU mode - getting it there isn't the same as the touch - To enter DFU, plug in USB cable, hold Select+Menu until screen goes off, then press Select+Menu again. If iTunes is running, it will download WTF and then FIRMWARE file that launches Disk Mode, allowing firmware restore.